Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}-8x-7y &= 2 \\ 8x+6y &= -2\end{align*}$
Answer: We can eliminate $x$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-y = 0$ Divide both sides by $-1$ and reduce as necessary. $y = 0$ Substitute $0$ for $y$ in the top equation. $-8x-7( 0) = 2$ $-8x = 2$ $-8x = 2$ $x = -\dfrac{1}{4}$ The solution is $\enspace x = -\dfrac{1}{4}, \enspace y = 0$.